2024/07/18 by Daniel van Huyssteen, Felipe López Rivarola, van Huyssteen, Daniel +5
Computer Science · Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Geometry and Mesh Generation #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2407.13665
openalex publication_date 2024/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mesh flexibility offered by the virtual element method through the permission of arbitrary element geometries, and the seamless incorporation of `hanging' nodes, has made the method increasingly attractive in the context of adaptive remeshing. There exists a healthy literature concerning error estimation and adaptive refinement techniques for virtual elements while the topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The creation of a quasi-optimal mesh is based on the principle of quasi-even error distribution over the elements which inherently relies on localized refinement and coarsening techniques. Thus, necessitating a fully adaptive remeshing procedure. In this work a novel fully adaptive remeshing procedure for the virtual element method is presented. Additionally, novel procedures are proposed for the identification of elements qualifying for refinement or coarsening based on user-defined targets. Specifically, a target percentage error, target number of elements, or target number of nodes can be selected. Numerical results demonstrate that the adaptive remeshing procedure can meet any prescribed target while creating a quasi-optimal mesh. The proposed fully adaptive procedure is of particular interest in engineering applications requiring an efficient simulation of a given accuracy, or desiring a simulation with the maximum possible accuracy for a given computational constraint.